% This is a Beamer template.  The top part of it is all the preamble, required to make the code run, set macros, etc.  Just ignore it if you'd like, and move down to "\title".  Otherwise, note that the "%" symbol makes whatever I type after it a comment.  If there is some code below that you want LaTeX to use, just delete the "%" before it.

\documentclass{beamer} % Put "\documentclass[handout]{beamer}" to change the output from slides to a pdf 'handout' (all frames are collasped).

% Here is where the various packages, etc., are set.

\mode<presentation>
\usefonttheme{professionalfonts}
\usetheme{Warsaw} % There are other themes available online, if you don't like this one.
\setbeamercovered{transparent}
\usepackage{etex}
\usepackage[english]{babel}
\usepackage[latin1]{inputenc}
\usepackage{times}
\usepackage[T1]{fontenc}
\usepackage[all]{xy}
\usepackage{graphicx,amsmath,amssymb}

% ----------------------------------------------------------------

\vfuzz2pt % Don't report over-full v-boxes if over-edge is small
\hfuzz2pt % Don't report over-full h-boxes if over-edge is small

% THEOREMS -------------------------------------------------------

% (Only change the following if you want to modify how Beamer handles definition, theorem, etc., environments.)

%\theoremstyle{plain}

%\newtheorem{theorem}{Theorem}[section]
%\newtheorem{proposition}[theorem]{Proposition}
%\newtheorem{conjecture}[theorem]{Conjecture}
%\newtheorem{corollary}[theorem]{Corollary}
%\newtheorem{lemma}[theorem]{Lemma}

%\theoremstyle{definition}
%\newtheorem{definition}[theorem]{Definition}
%\newtheorem{example}[theorem]{Example}
%\newtheorem{remark}[theorem]{Remark}
%\newtheorem{condition}[theorem]{Condition}
%\newtheorem{notation}[theorem]{Notation}
%\newtheorem{question}[theorem]{Question}
%\numberwithin{equation}{section}


% MATH MACROS -----------------------------------------------------------

% (Here you can set up macros (coding shortcuts) to help type thing faster.  For example, the real numbers symbol is $\mathbb{R}$.  I often use $\RR$ instead, but I had to set that macro up here:

\newcommand{\CC}{{\mathbb{C}}}  %complex numbers
\newcommand{\NN}{{\mathbb{N}}}  %natural numbers
\newcommand{\PP}{{\mathbb{P}}}  %projective space
\newcommand{\QQ}{{\mathbb{Q}}}  %rational numbers
\newcommand{\RR}{{\mathbb{R}}}  %real numbers
\renewcommand{\SS}{{\mathbb{S}}} %sphere
\newcommand{\TT}{{\mathbb{T}}}  %torus
\newcommand{\ZZ}{{\mathbb{Z}}}  %integers


% ----------------------------------------------------------------

% This is where your title, etc., go.

\title[MTH 499 Capstone Project]
{This is our title for the project}
\author{Jordan Watts}
\institute{Central Michigan University}
\date{\today}

% Now begins the actual document.

\begin{document}

% Create a title page.

\begin{frame}
  \titlepage
\end{frame}

% Below is a sample slide from a talk I gave recently.

\begin{frame}{This Frame's Title}

\begin{itemize}  %Itemizing is not something you have to use, but sometimes helps to break up a paragraph into readable bits.

\item Fix $\alpha \in \RR \smallsetminus \QQ$.

\pause %This creates a slide with only what you have typed so far, pausing the rest of what is typed up in this frame.

\item Let $\ZZ^2$ act on $\RR$ by $$(m,n)\cdot x = x+m+n\alpha.$$

\pause

\item The orbits are dense, and so the orbit space $T$ has trivial topology.

\pause

\item $T$ is a group, but would not typically be considered a topological group.

\pause

\item Is there a ``differentiable structure'' that we could equip $T$ with?

\end{itemize}

\end{frame}

\end{document} 